A novel photonic-assisted approach to microwave frequency measurement is proposed and experimentally demonstrated. The proposed scheme is based on the frequency-to-power mapping with different transmission responses. A polarizer is used in one output branch of a phase modulator to simultaneously implement phase modulation and intensity modulation. Owing to the complementary nature of the transmission responses and the Mach-Zehnder interferometers (MZIs), this scheme theoretically provides high resolution and tunable measurement range. The measurement errors in the experimental results can be kept within 0.2 GHz over a frequency range from 0.1 to 5.3 GHz.